Note: You missed to add some basic information of the perpendicular line or missed the answer options, hence I am solving using a sample equation but it would clear your concept.
Answer:
Please check the attached graph.
Step-by-step explanation:
We know the slope-intercept form of line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given the points
Finding the slope between F(1, 8) and G(-3, -4)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-4\right)[/tex]
[tex]m=\frac{-4-8}{-3-1}[/tex]
[tex]m=3[/tex]
Thus, the slope of the line FG = m = 3
From the given line, we can also determine the y-intercept 'b' by setting x = 0 and checking the corresponding y value.
i.e. at x = 0, y = 5
Thus, y-intercept b = 5
so substituting m = 3 and b = 5 in the slope-intercept form
y = mx+b
y = 3x+5
Therefore, the equation of line FG will be:
Please check the attached diagram, where the red line represents the line y=3x+5
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.
Slope of Perpendicular line = -1/m = -1/3
Thus, any line with the slope m = -1/3 would be the line that will be perpendicular to line FG
Let say the line with the slope m = -1/3 and y-intercept 2
y = -1/3x + 5
Please check the attached graph, the blue line is representing the perpendicular line y = -1/3x + 5 to line FG
The graph of both lines is clearly representing that the line y = -1/3x + 5 is perpendicular to line FG.
